Black hole anatomy

I know there are several theories as to what may be inside black holes and that the standard model usually describes the geometry with a singularity surrounded by an event horizon and then a photon sphere.
Three questions:

Is there an easy way to calculate the distance and or ratios between the three?

Does the singularity have an actual size (diameter) like the other two?

Is the singularity always a point or are there any theories that model the singularity with an actual diameter that continues to grow as it accumulates matter?

Singularities aren't well described by modern physics. General Relativity can describe the area around a singularity (a black hole), but the mathematics of GR give nonsensical answers at the singularity itself.

In terms of mathematics of the distance and ratios; yes, but I don't know them and 'an easy way to calculate' is probably not realistic: Einstein was a genius for a reason. The event horizon is simply the point around a mass where the escape velocity = c (the speed of light). While I know that some speculative physics models describe singularities differently (String Theory in particular), I believe the quasi-accepted current view on singularities is that they are points of no diameter and of infinite density.

How does the swarzchild radius describe the relation of all three? Is there some proportionality between their radiuses?
This question becomes more interesting if we imagine a singularity with a finite density and therefore an actual diameter. How then would the three diameters compare?

What if we just assume it is like any other mass? The fact that its g has an escape velocity of c doesn’t necessarily mean the body of the black hole has to be a point. If the singularity had a finite density and therefore a diameter would there be a way to calculate that diameter based on the mass?

What if we just assume it is like any other mass? The fact that its g has an escape velocity of c doesn’t necessarily mean the body of the black hole has to be a point. If the singularity had a finite density and therefore a diameter would there be a way to calculate that diameter based on the mass?

Once you have enough mass in small enough an area to form a black hole, the pressure required to keep the matter collapsing actually increases the gravity, so that it becomes fundamentally impossible for any amount of pressure to prevent the collapse.

Why is pressure required to keep the matter collapsing? Did you mean keep the matter FROM collapsing? If something becomes 100% dense (as I believe the singularity to be) and cannot get any denser then how can it collapse any farther? And why would it need pressure to keep it from collapsing?

To expand on this response (to make it even vaguely useful), the event horizon, photon sphere, and other interesting surfaces can all be easily calculated in GR for any type of black hole---with the different surfaces generally expressed in terms of the Schwarzschild radius (and other fundamental parameters, i.e. spin and charge).

The fact that its g has an escape velocity of c doesn’t necessarily mean the body of the black hole has to be a point.

According to GR, the central mass does need to be a point. Not only is the escape velocity equal to 'c'; but also, space-time is so distorted inside the event horizon that the only direction a particle can move is inward (i.e. its 'impossible' to even stay still--like on a hard surface).

Why is pressure required to keep the matter collapsing? Did you mean keep the matter FROM collapsing? If something becomes 100% dense (as I believe the singularity to be) and cannot get any denser then how can it collapse any farther? And why would it need pressure to keep it from collapsing?

He did mean "keep the matter 'from' collapsing". Pressure is always required to keep material from collapsing. The reason the earth doesn't collapse, or the air in the room, or the table your typing on---are because of pressure. Once inside the event horizon there is no pressure strong enough to resist collapse (according to general relativity). There is no such thing as '100%' dense---something can become arbitrarily dense because it can become arbitrarily small.

People think that a new quantum theory of gravity might be able to explain what actually happens at the singularity. Most string theorists, for example, think that at some point the matter will reach a maximum density (and minimum size), at about the planck scale---[itex]\sim 10^{-35} m[/itex]; but no one really knows.

An additional thing to note is that charged and rotating black-holes have singularities that aren't points. A rotating black hole (called a "Kerr black hole") actually has a torus-shaped singularity (again, according to GR) with a finite, calculable size.

I realize pressure is required to keep stars and anything else that may have space inside from collapsing. My point is that a singularity MAY be as dense as anything can be. It can't collapse anymore and therefore would need no pressure to support it. If this were possible then the singularity would have an actual size and would be growing proportionately just like the event horizon and photon sphere. My original question was how could you calculate the diameter of the singularity? Hypothetically speaking.

How can it collapse further and why does it have to? Can't a black hole be so dense that there is no space left inside? An area filled 100% complete with the smallest partials the universe has to offer. There would be no more area to collapse to.

I realize my original question most likely cannot be answered because we don’t know how small those first particles are or how many have accumulated in the black hole. Could there be some indirect way to calculate backwards from the observed mass and event horizon and come up with either a diameter for the singularity or something.

Well ignoring GR whilst trying to calculate black hole information is like asking someone what color a house is without looking at it, but I can address your other point.

Fundamental Particles don't really have a size, when you start getting down to the level where the size of a Fundamental particle becomes non-trivial, the uncertainty principle takes over. Basically a fundamental particle is a point-particle which means it is zero-dimensional (no size), but the uncertainty principle enters in and instead of a single point where the particle definitely is, you have a range of different points where the particle could be located (if that didn't make sense search the forums, someone has explained it better than me). A simple way of looking at it is that as density increases the width of those possible locations of the particle gets smaller. Within a black hole the gravitational force is so great that no force in the universe (that we know of) is strong enough to counter the inward push of gravity. So normally when particles are pushed together, the probability clouds of the particles (meaning the patch where the particle could be) get smaller until some other force (electromagnetic, strong, weak) pushes outwards and balances the force of gravity. However in a black hole, there is no force strong enough to counter the push of gravity so the probability waves of the particles get infinitely small.

Why is pressure required to keep the matter collapsing? Did you mean keep the matter FROM collapsing? If something becomes 100% dense (as I believe the singularity to be) and cannot get any denser then how can it collapse any farther? And why would it need pressure to keep it from collapsing?

Yes, I meant keep from collapsing, sorry. If you don't have outward pressure, the inward force of gravity will force the matter to collapse. And no, having the matter simply orbit doesn't work, as there are no stable orbits close to a black hole, let alone inside it.

Just to clarify, GR Is well behaved within the event horizon, its only near the singularity that it breaks down. In the case of a rotating or charged black hole, it can be a little worse.

While it is indeed true that General Relativity provides a sensible description of space-time inside the event horizon but outside the singularity, this doesn't mean we can trust it. In order to avoid the singularity, after all, General Relativity has to give an incorrect description of the black hole some distance outside that singularity. How far outside? We don't yet know. My expectation is that it may go as far as the event horizon, because the horizon itself forces quantum effects to have a significant impact on the behavior of the black hole. We think we understand the quantum behavior of the horizon itself. But that makes me doubt any of the non-quantum predictions of what goes on even just inside.

I understand pressure is required to supports a balloons surface but not so simple on a bowling ball. Why is pressure needed on a complely solid object?

Well, consider a chunk of the matter. There will be a force inward caused by the gravitational attraction. If that force is not balanced by something, that force inward will cause the matter to accelerate inward. So if the matter is not collapsing, there must be a force outward to counterbalance the inward force of gravity. That force is a pressure.